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Easy geo problem

Source: Tuymaada 2016. junior league\ P2

July 22, 2016
geometry proposedgeometry

Problem Statement

The point DD on the altitude AA1AA_1 of an acute triangle ABCABC is such that ∠BDC=90∘\angle BDC=90^\circ; HH is the orthocentre of ABCABC. A circle with diameter AHAH is constructed. Prove that the tangent drawn from BB to this circle is equal to BDBD.
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